Signal information received by a radar system frequently includes unwanted echoes reflected from stationary or slowly moving reflectors such as the ground or sea, or from wind driven rain or chaff. The unwanted echoes obscure desired signals--such as those reflected from a moving target. The desired signal usually varies quickly with time, whereas the unwanted signals vary slowly with time. This difference can be exploited to eliminate the unwanted signals because data pulses corresponding to quickly varying signals are un-correlated as a function of time whereas slowly varying signals are correlated with time. In other words, stationary reflectors yield return echoes that include frequency components which vary more slowly than the frequency components of the desired moving target. Therefore, unwanted signals can be reduced or eliminated by canceling the time-correlated components from the received signals.
To this end, various systems and techniques have been devised which filter unwanted signals by isolating the correlated components of a received signal and then canceling the correlated components from the received signal. One such system is a numeric filter that adapts to the estimated statistical characteristics of input or output signals (see generally, R. A. Monzingo and T. W. Miller, Introduction to Adaptive Arrays, (John Wiley and Sons, New York, 1980), Chap. 8). A particular embodiment of an adaptive processor is an space-time adaptive canceler which yields one filtered output channel from a plurality of sensor output channels. The space-time adaptive canceler obtains weight factors corresponding to the coherent output from each sensor channel and then combines the weighted outputs to yield one output channel. With properly chosen weight factors, the noise elements of the sensor channels are reduced or eliminated.
FIG. 1 illustrates the general form of a space-time adaptive canceler which decorrelates or statistically orthogonalizes the time samples of a group of auxiliary channels from a main channel. The auxiliary channels are linearly weighted such that the output noise power residue of the main channel is minimized. This is equivalent to statistically orthogonalizing the auxiliary channels with respect to the main channel. In FIG. 1 the main channel input is designated x.sub.0, and the auxiliary channels are designated x.sub.n, n=1, 2, . . . , N-1, with the number of auxiliary channels, N-1, further dnoted N.sub.aux. The signals received from the auxiliary sensors are sampled L times at equal intervals of T seconds. The main sensor is also sampled in time and can be delayed by an arbitrary time delay .tau..
The time-delayed sample of the nth auxiliary input channel designated by a row vector x: EQU x.sub.n =(x.sub.n (t),x.sub.n (t-T), . . . ,x.sub.n (t-(L-1)T)) (1)
with the optimal weight row vector w.sub.n for x.sub.n represented by EQU w.sub.n =(w.sub.1n, w.sub.2n, . . . w.sub.Ln). (2)
A LN.sub.aux length column vector, X, comprising all auxiliary input data is EQU X=(x.sub.1, x.sub.n, . . . x.sub.Naux).sup.T, (3)
where T denotes the vector transpose operation. A LN.sub.aux length optimal weight column vector W comprising all auxiliary weights is EQU W=(w.sub.1, w.sub.2, . . . w.sub.Naux).sup.T. (4)
R.sub.xx represents the LN.sub.aux .times.LN.sub.aux input covariance matrix of the auxiliary inputs and r is the LN.sub.aux length cross-covariance vector between the main and the LN.sub.aux auxiliary inputs, or more formally, EQU R.sub.xx =E{X*X.sup.T }, (5) EQU r=E{X*x.sub.0 }, (6)
where E{.multidot.} denotes the expected value.
The vector, W, therefore, is the solution of the linear vector equation: EQU R.sub.xx W=r. (7)
(Again, see generally, R. A. Monzingo and T. W. Miller, Introduction to Adaptive Arrays, (John Wiley and Sons, New York, 1980), Chap. 8.)
Also, since the time-delayed samples from each auxiliary channel are statistically stationary, the L.times.L covariance matrix R.sub.XnXn of the nth auxiliary channel, EQU R.sub.XnXn =E{x.sub.n *x.sub.n.sup.T }, (8)
R.sub.XnXn is a hermitian toeplitz matrix having the form: ##EQU1##
A space-time adaptive cancellation method first solves equation (7) for the optimal decorrelation weights by exploiting the fact that matrix R.sub.XnXn is a hermitian toeplitz matrix, then applies the weights, as shown in FIG. 1, to produce one filtered output channel.
In a Gram-Schmidt canceler the optimal weights formulated by Equation (7) are not computed, rather the data in the input channels are filtered directly through an orthogonalization network. The steady state output residue is the same as if the weights were separately calculated using Equation (7) and then applied to the input data set.
FIG. 2 shows a general M-input open loop Gram-Schmidt canceler with y.sub.0, y.sub.1 . . . ,y.sub.M-1 representing the complex data in the 0th, 1st, . . . ,M-1th channels, respectively, where y.sub.0 is the main channel, and the remaining M-1 inputs are the auxiliary channels. The Gram-Schmidt canceler sequentially decorrelates each auxiliary input channel from the other input channels by using the two-input decorrelation canceler shown in FIG. 3. For example, as seen in FIG. 2, in the first level of decomposition, y.sub.M-n is decorrelated with y.sub.0, y.sub.1, . . . ,y.sub.M-2. Next, the output channel resulting from the decorrelation of y.sub.M-1 with y.sub.M-2 is decorrelated with the other outputs of the first level decorrelation processors. This decomposition process is repeated until one final output channel remains.
More specifically, with y.sub.n.sup.(m) representing the output of the decorrelation processors on the mth level, the output of the decorrelation processors of the m+1th level are given by: ##EQU2## wherein that y.sub.n.sup.(1) =y.sub.n. The weight w.sub.n.sup.(m), seen in Equation (10), is computed to decorrelate y.sub.n.sup.(m+1) with y.sub.M-m.sup.(m). Since the decorrelation weights in each of the decorrelation processors are computed from a finite number of input samples rather than an infinite number, the decorrelation weights are only estimates of the optimal weights discussed above in connection with Equation (2). For K input samples per channel, weight w.sub.n.sup.(m) is estimated as ##EQU3## where * denotes the complex conjugate, .vertline..multidot..vertline. is the magnitude, and k indexes the sampled data.
Examples of adaptive processors and components thereof include U.S. Pat. No. 4,149,259 (Kowalski) which discloses to an adaptive processor employing a transverse filter for convoluted image reconstruction; U.S. Pat. No. 4,196,405 (Le Dily et al.) which discloses an adaptive processor utilizing a transverse filter particularly adapted to the filtering of noise from the transmission of data over telephone lines; U.S. Pat. No. 4,459,700 (Kretschmer, Jr. et al.) which discloses a moving target indicator system employing an adaptive processor; U.S. Pat. No. 3,952,188 (Sloate et al.) which discloses an adaptive processor utilizing a monolithic transverse filter; U.S. Pat. No. 4,038,536 (Feintuch) which discloses an adaptive processor utilizing a recursive least mean square error filter and U.S. Pat. No. 4,489,320 (Lewis et al.) which discloses a moving target indicator system utilizing an adaptive processor. Other patents directed to related techniques include: U.S. Pat. No. 4,489,392 (Lewis) which discloses a orthogonalizer for filtering in phase and quadrature digital data; U.S. Pat. No. 4,222,050 (Kiuchi et al.) which discloses a Moving Target Indicator System and U.S. Pat. No. 4,471,357 (Wu et al.) which discloses a transverse filter for use in filtering the output from a synthetic aperture radar system.